# Graph Isomorphism Restricted by Lists

@article{Klavk2016GraphIR, title={Graph Isomorphism Restricted by Lists}, author={Pavel Klav{\'i}k and Du{\vs}an Knop and Peter Zeman}, journal={ArXiv}, year={2016}, volume={abs/1607.03918} }

The complexity of graph isomorphism (GraphIso) is a famous unresolved problem in theoretical computer science. For graphs $G$ and $H$, it asks whether they are the same up to a relabeling of vertices. In 1981, Lubiw proved that list restricted graph isomorphism (ListIso) is NP-complete: for each $u \in V(G)$, we are given a list ${\mathfrak L}(u) \subseteq V(H)$ of possible images of $u$. After 35 years, we revive the study of this problem and consider which results for GraphIso translate to…

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## References

SHOWING 1-10 OF 113 REFERENCES

### List H-Coloring a Graph by Removing Few Vertices

- MathematicsAlgorithmica
- 2016

The conjecture that DL-Hom is fixed-parameter tractable for the class of graphs H for which the list homomorphism problem (without deletions) is polynomial-time solvable is conjectured.

### Graph Isomorphism for Bounded Genus Graphs In Linear Time

- MathematicsArXiv
- 2015

This work improves previously known algorithms whose time complexity is $n^{O(g)}$ and is the first fixed-parameter tractable algorithm for the graph isomorphism problem for bounded genus graphs in terms of the Euler genus.

### Algorithmic Aspects of Regular Graph Covers with Applications to Planar Graphs

- MathematicsICALP
- 2014

Inspired by Negami, the structural results used by Babai in the 1970's are applied to study automorphism groups of graphs to get the complete structural understanding of regular covers for 2-cuts.

### Isomorphism of (mis)Labeled Graphs

- MathematicsESA
- 2011

It is shown that for every fixed integer k, the algorithm solving the graph isomorphism problem for pairs of input graphs which are close with respect to the measure can decide in quadratic time whether a labeled graph G can be obtained from another labeled graph H by relabeling at most k vertices.

### Restricted space algorithms for isomorphism on bounded treewidth graphs

- Mathematics, Computer ScienceInf. Comput.
- 2009

### Structure theorem and isomorphism test for graphs with excluded topological subgraphs

- MathematicsSTOC '12
- 2012

It is proved that for a fixed H, every graph excluding H as a topological subgraph has a tree decomposition where each part is either "almost embeddable" to a fixed surface or has bounded degree with the exception of a bounded number of vertices.

### Isomorphism on Subgraph-Closed Graph Classes: A Complexity Dichotomy and Intermediate Graph Classes

- MathematicsISAAC
- 2013

It is shown that there is a complexity dichotomy in case the set of forbidden subgraphs is finite and the problem is polynomial-time solvable if the forbidden set contains a forest of subdivided stars and is graph isomorphism complete otherwise.

### Finding Small Weight Isomorphisms with Additional Constraints is Fixed-Parameter Tractable

- MathematicsIPEC
- 2017

The problem of deciding whether there is an isomorphism between two graphs that moves k vertices and satisfies Lubiw-style constraints is in FPT, with k and the size of $R$ as parameters.

### Isomorphism testing for graphs of bounded genus

- MathematicsSTOC '80
- 1980

This result is noteworthy for at least two reasons: first, it extends the polynomial time isomorphism results for the plane [HT 72] and also the projective plane [L 80] to arbitrary surfaces and secondly it gives one of the few known natural decompositions of the isomorphicism problem into an infinite hierarchy of problems.